Model fitting by least squares

The first level of computer use in science and engineering is ``modeling."
Beginning from physical principles and design ideas,
the computer mimics nature.
After this, the worker looks at the result and thinks a while,
then alters the modeling program and tries again.
The next, deeper level of computer use is that the computer itself
examines the results of modeling and reruns the modeling job.
This deeper level is variously called ``fitting" or ``inversion."
The term ``processing" is also used, but it is broader,
including the use of adjoint operators (as discussed in
chapter
).
Usually people are more effective than computers at fitting or inversion,
but some kinds of fitting are more effectively done by machines.
A very wide range of methods
comes under the heading of ``least squares,''
and these methods are the topic of this chapter and
chapters through .

A part of basic education in mathematics
is the fitting of scattered points on a plane
to a straight line.
That is a simple example of inversion,
a topic so grand and broad that
some people think of learning to do inversion as simply ``learning.''
Although I will be drawing many examples
from my area of expertise,
namely,
earth soundings analysis,
the methods presented here
are much more widely applicable.